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Subfactor categories of triangulated categories

2014/04/19 by Jinde Xu, Xu, Jinde, Panyue Zhou +3
Mathematics · #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1404.4930

openalex publication_date 2014/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \cal T be a triangulated category, \cal A a full subcategory of \cal T and \cal X a functorially finite subcategory of \cal A. If \cal A has the properties that any \cal X-monomorphism of \cal A has a cone and any \cal X-epimorphism has a cocone. Then the subfactor category \cal A/[X] admits a pretriangulated structure in the sense of [BR]. Moreover the above pretriangulated category \cal A/[X] with (\cal X,\cal X[1]) = 0 becomes a triangulated category if and only if (\cal A,\cal A) forms an \cal X-mutation pair and \cal A is closed under extensions.

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